Gelfand pairs associated with the action of graph automaton groups

Document Type : Ischia Group Theory 2020/2021


1 Dipartimento di Ingegneria, Università degli Studi Niccolò Cusano, Via Don Carlo Gnocchi, 3, 00166, Roma, Italy

2 Università degli Studi Niccolò Cusano Dipartimento di Ingegneria Via Don Carlo Gnocchi, 3 00166 Roma, Italy


Graph automaton groups constitute a special class of automaton groups constructed from a graph. In this paper, we show that the action of any graph automaton group on each level of the rooted regular tree gives rise to a Gelfand pair. In particular, we determine the irreducible submodules of the action of such a group on the space of functions defined on each level of the tree, and we exhibit the corresponding spherical functions.


Main Subjects

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Volume 12, Issue 2 - Serial Number 2
Proceedings of the Ischia Group Theory (2020/2021) - Part 2
June 2023
Pages 55-66
  • Receive Date: 03 December 2021
  • Revise Date: 29 January 2022
  • Accept Date: 04 February 2022
  • Published Online: 01 June 2023